A013706 Decimal expansion of 2*Sum_{k=1..50000} (-1)^(k-1)/(2k-1).

1, 5, 7, 0, 7, 8, 6, 3, 2, 6, 7, 9, 4, 8, 9, 7, 6, 1, 9, 2, 3, 1, 3, 2, 1, 1, 9, 1, 6, 3, 9, 7, 5, 2, 0, 5, 2, 0, 9, 8, 5, 8, 3, 3, 1, 4, 6, 8, 7, 5, 5, 7, 9, 6, 2, 5, 8, 7, 4, 4, 5, 2, 6, 8, 5, 0, 4, 1, 0, 7, 5, 6, 4, 1, 2, 2, 1, 6, 5, 3, 4, 8, 1, 2, 3, 5, 6, 6, 2, 0, 9, 0, 5, 5, 0, 9, 7, 3, 5, 2, 6, 8, 8, 4, 3, 6, 3, 2, 7, 4, 2, 5, 0, 9, 3, 7, 0, 4, 8, 2, 5, 0, 6, 1, 9, 3

Offset

1,2

Comments

A deceptively correct-looking approximation to Pi/2.

Links

Table of n, a(n) for n=1..126.

J. M. Borwein, P. B. Borwein and K. Dilcher, Pi, Euler numbers and asymptotic expansions, Amer. Math. Monthly, 96 (1989), 681-687.

J. M. Borwein, P. B. Borwein and K. Dilcher, Pi, Euler numbers and asymptotic expansions, Amer. Math. Monthly, 96 (1989), 681-687.

J. M. Borwein and R. M. Corless, Review of "An Encyclopedia of Integer Sequences" by N. J. A. Sloane and Simon Plouffe, SIAM Review, 38 (1996), 333-337.

Example

Pi/2:     1.570796326794896619231321691639751442098584699687552910487472...
This sum: 1.570786326794897619231321191639752052098583314687557962587445...
..........================^=================^^^======^^^^=====^=^^^===^^...

Mathematica

RealDigits[2*Sum[(-1)^(k-1)/(2k-1), {k, 50000}], 10, 130][[1]] (* Harvey P. Dale, Oct 23 2012 *)

Crossrefs

Cf. A000796, A216542, A013706, A216543, A216544, A216545, A013705, A216546, A216547, A216548.

Cf. also A013707, A195793.

Sequence in context: A295823 A161018 A197254 * A195793 A216545 A216547

Adjacent sequences: A013703 A013704 A013705 * A013707 A013708 A013709

Keyword

cons,nonn,easy,nice,changed

Author

N. J. A. Sloane

Extensions

Entry revised by N. J. A. Sloane, Sep 08 2012

Status

approved